That's not the way the TPE works.
First of all, the TPE is not a "thing", and it can't be traded to other teams. It is simply an allowance that lets you bring in salary that you don't have to match. You can use it to sign a player, or to acquire a player from another team without sending anyone back. However, you cannot package it in a bigger trade.
So, how about no? 
In real world terms, though... if we made a trade with another team that was over the cap. Let's say we took on a player earning $10M and a first-round draft pick, and sent back a 2nd rounder or a conditional pick or something. We could absorb that player without having to send salary back out, because of the TPE.
That then creates a *new* TPE for the other team, right, since they sent out $10M and took back no salary?
Technically, you're not trading the TPE. But, it basically works the same, in that you're creating a new one, which is even better because it's resetting the one-year clock.
Am I missing something? This is, of course, predicated on the other team having an expiring contract they're looking to dump.
But I agree, you aren't going to take on an $8M or $10M salary for a guy you don't want, just for a late pick. The next JuJuan/Giddens/Fab Melo ain't worth that much!